"We have a common commitment to combating terrorism and achieving economic prosperity," she said.
"It is true we are different countries with different backgrounds. We will from time to time disagree. But we believe our differences are far outweighed by the bondage," Clinton said, addressing students and opinion makers at Anna Centenary Library here.
Beginning her speech with the Tamil word ''Vanakkam'' (namaste) amid applause from the gathering, she said the US was watching the progress of India with "great admiration" as the country maintained the democratic foundations and worked for improving the lives of the poor.
Clinton said President Barack Obama, in his address to Indian Parliament last year, had said the relationship between India and US would be one of "defining partnership of the 21st century."
Clinton, who is in India for the second India-US Strategic Dialogue, said the US had a great commitment to government-to-government relationship and a greater commitment to people-to-people relationship.
She also said the US was betting high on India's future and opening of its markets to the world would bring more prosperity to India and South Asia.
Lauding India's firm commitment to democracy, Clinton said Indian leadership should continue to engage the Myanmarese government, whose treatment of its own people was deplorable, to secure the release of all political prisoners.
Touching upon the Sri Lankan Tamils' issue, she said every citizen of the island nation deserved equal help and opportunity. The two countries should work together to combat piracy and for maritime security, she said.
Speaking about India's growing leadership in the world, Clinton said India and the US could more productively engage in complex global issues and support democratic transitions in Middle East and North Africa.
Clinton also advocated more economic cooperation among India, US and China, though she maintained it was "not easy".